Question 194976: Using each number only once, complete the first and second fraction to make a true sentence. (1, 3, 9, 10)
__ / __ (+ or -) __ / __ = 23/20
This is a problem my daughter has to complete for her math homework. I have tried it every way and am stumped!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Don't feel bad about being stumped. That's because there is no solution to the problem as stated.
Here's why. Let's use a, b, c, and d to represent the 4 numbers because we don't know where they go yet. So we have:
Now let's apply the lowest common denominator and add the fractions:
 where k is some multiplier. k can't be 1 because no pair of the given numbers has a product of 20, so our problem becomes:
}{kbd} = \frac{23}{20})
So, if the denominators are:
10 and 1, the product is 10 and 
10 and 3, the product is 30 and 
10 and 9, the product is 90 and 
3 and 1, the product is 3 and 
3 and 9, the product is 27 and 
9 and 1, the product is 9 and 
Now, before we go any further, realize that if a, b, c, and d are integers, then  must also be an integer. So let's let  to simplify things for the moment.
If , then  and x is not an integer.
If , then  and x is not an integer.
x is not an integer for any of the other values either, but you can check that for yourself if you like.
Therefore, the problem cannot be solved. Q.E.D.
John
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